Action-angle coherent states for quantum systems with cylindric phase space

TL;DR

This paper develops quantum coherent states for systems with cylindric phase space, such as a particle on a circle, using different probability distributions to construct and analyze quantizations.

Contribution

It introduces a method to build quantum coherent states for cylindric phase spaces from various probability distributions, expanding the tools for quantization of such systems.

Findings

Gaussian-based coherent states are constructed and analyzed.

Uniform distribution-based states are explored for quantization.

Different probability distributions lead to distinct quantization schemes.

Abstract

Quantum versions of cylindric phase space, like for the motion of a particle on the circle, are obtained through different families of coherent states. The latter are built from various probability distributions of the action variable. The method is illustrated with Gaussian distributions and uniform distributions on intervals, and resulting quantizations are explored.